Of late, reduction gears which work by taking advantage of the difference in the number of teeth have been put into practical use. First, the outline of this reduction gear has been described with reference to FIG. 1. Numeral 1 designates a wave generator on the periphery of which a roller group 2 is arranged. Further, a flex spline 3 is arranged in the form to circumscribe this roller group 2. This flex spline 3 has teeth (Z.sub.1 in numbered) formed on the circumference thereof. This flex spline 3 meshes with the inside teeth (Z.sub.2 in number) of the circular spline 4 arranged at the outermost periphery. The relation between Z.sub.1 and Z.sub.2 is Z.sub.1 &lt;Z.sub.2 or Z.sub.1 &gt;Z.sub.2, with the difference between the numbers of teeth Z.sub.1 and Z.sub.2 being an even number. The outside circumference of the flex spline 3 and the inside circumference of the circular spline 4 mesh with each other at two positions on their circumferences. Now, as the wave generator 1 makes one turn, the relative positions of the circular spline 4 and the flex spline 3 are shifted by an angle corresponding to the number of teeth of (Z.sub.2 -Z.sub.1)/2. A reduction gear of this composition needs to have its flex spline 3 and circular spline 4 formed in elliptical shapes, thus involving difficulties in its manfacturing process and in ensuring the accuracy with which they are formed. Thus, because of the difficulty achieving accuracy informing parts, there was a need of selecting acceptable products only when these parts are to be assembled, which led to high cost.
Then, in order to make this principle realizable, generally, a bearing which is deformable in the radial direction is employed (FIG. 2). Thus, numeral 5 designates a wave generator, on the outside circumference of which a bearing 6 is used, said bearing being so arranged that its inside diameter is lightly pressured in over wave generator 5. This bearing 6 consists of inner ring 6a, outer ring 6b, balls 6c and retainer 6d, and is deformable in the radial direction. On the outside circumference of the aforementioned bearing 6, there is arranged a flex spline 7 and on the outside circumference of this flex spline 7, teeth (Z.sub.1 in number) are formed. Further, on the outside circumference of the flex spline 7, circular splines 8 and 9 are located and the internal teeth (Z.sub.2 in number) of the circular spline 8 and likewise the internal teeth (Z.sub.3 in number) of the circular spline 9 mesh with the external teeth of the flex spine 7. The relationships between the numbers of teeth Z.sub.1, Z.sub.2 and Z.sub.3 are such that Z.sub.1 &lt;Z.sub.2, Z.sub.1 =Z.sub.3 and the difference in the numbers of teeth Z.sub.1 -Z.sub.2 is an even number. In this reduction gear, an elliptical shape is obtainable by deforming the bearing 6; therefore, the problem of achieving high accuracy in forming the contacting surfaces of balls may be solved. However, no improvement is apparent in the requirement that the meshing of the teeth of the flex spline 7 and those of the circular splines 8 and 9 must be made without a gap. In manufacturing or assembling this reduction gear, it is necessary to eliminate the variation in the axial thickness of the bearing 6, also to make zero the variation in the radial distance between the internal diameter of the flex spline 7 and its outer circumferential meshing pitch circle A (FIG. 3) and, further, to ensure perfect out of roundness of the meshing pitch circle B of the internal teeth of the circular splines 8 and 9 (FIG. 4).
Such arrangements are virtually impossible to achieve in manufacture, however, and even if proper combinations have been worked out, dimensional errors cannot be compensated for anywhere; consequently, a problem of stoppage of wave generator 5 will arise. Then, if the dimensions of parts have been set with the dimensional errors taken into account in order to avoid this, naturally, backlash will develop, rendering it unusable as a reduction gear for precision devices such as industrial robots, etc.